Hypersurfaces in Teichmuller Space and the Geodesic Length Spectrum
نویسنده
چکیده
We investigate the subset E of Teichmuller space consisting of all surfaces which have at least two closed simple geodesics of the same length. Using elementary methods from the theory of surfaces we show that E is baire meagre but its complement, N , contains no arcs.
منابع مشابه
Hoph Hypersurfaces of Sasakian Space Form with Parallel Ricci Operator Esmaiel Abedi, Mohammad Ilmakchi Department of Mathematics, Azarbaijan Shahid Madani University, Tabriz, Iran
Let M^2n be a hoph hypersurfaces with parallel ricci operator and tangent to structure vector field in Sasakian space form. First, we show that structures and properties of hypersurfaces and hoph hypersurfaces in Sasakian space form. Then we study the structure of hypersurfaces and hoph hypersurfaces with a parallel ricci tensor structure and show that there are two cases. In the first case, th...
متن کاملLength series on Teichmuller space
We prove that a certain series defines a constant function using Wolpert’s formula for the variation of the length of a geodesic along a Fenchel Nielsen twist. Subsequently we determine the value viewing it as function on the the Deligne Mumford compactification M1,1 and evaluating it at the stable curve at infinity. Conventions: 1. For γ an essential closed curve on a surface lγ(x) is the leng...
متن کاملQuantitative Recurrence and Large Deviations for Teichmuller Geodesic Flow
We prove quantitative recurrence and large deviations results for the Teichmuller geodesic flow on the moduli space Qg of holomorphic unit-area quadratic differentials on a compact genus g ≥ 2 surface.
متن کاملMultiplicities of Simple Closed Geodesics and Hypersurfaces in Teichmüller Space
Using geodesic length functions, we define a natural family of real codimension 1 subvarieties of Teichmüller space, namely the subsets where the lengths of two distinct simple closed geodesics are of equal length. We investigate the point set topology of the union of all such hypersurfaces using elementary methods. Finally, this analysis is applied to investigate the nature of the Markoff conj...
متن کاملThe asymptotic behavior of least pseudo-Anosov dilatations
Let S = Sg,n be an orientable surface with genus g and n marked points. The mapping class group of S is defined to be the group of homotopy classes of orientation preserving homeomorphisms of S. We denote it by Mod(S). Given a pseudo-Anosov element f ∈ Mod(S), let λ(f ) denote the dilatation of f (see section 2.1). We define L(Sg,n) := {log λ(f )|f ∈ Mod(Sg,n) pseudo-Anosov}. This is precisely ...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 1995